Cha~ter II

FUNDAMENTALS OF EXCHANGE TRADED OPTIONS

A. CHARACTERISTICS OF OPTIONS

i. Conventional OTC Options Compared to Listed Options

For many years options on stocks were sold only in the over-

the-counter ("OTC") market. The terms of these options contracts

-- often called conventional or OTC options -- were negotiated and

entered into between the individual buyer and seller through

broker-dealers with performance guaranteed by a NYSE member

broker-dealer. Generally, the conventional OTC option remained

outstanding until expiration because the individualized nature

of the conventional OTC options contract made trading these options

costly and difficult. Conventional OTC options are still being written

but the activity in these options has substantially declined with

the introduction o~ listed options trading.

Listed options differ from conventional O1]3 options in several

important ways including: i) a liquid secondary market exists

for the trading of listed options; 2) transaction costs associated with

listed options are lower than those for conventional OTC options;

and 3) up-to-date quotations and transaction prices on listed

options are obtainable, during the trading day, through quotation and

price reporting services found in brokerage firms; and closing prices

are available through newspapers.

(73)

The exercise rights of holders of conventional OI~ options are

against the particular seller of the options. To close a position

in a conventional OTC option requires that either the original parties

cancel the contract or that a buyer be found for the previously

negotiated contract, a cumbersome and costly process generally

transacted through brokers over the telephone. Closing transactions

in listed options are effected on an options exchange.

The secondary market in listed options is made possible

because all listed options contracts have standardized terms and

are issued and guaranteed by one organization, the Options Clearing

Corporation ("OCC"), which stands as intermediary between options

buyers and sellers. Because options contracts with standardized

terms are readily interchangeable, these contracts usually can be

traded with ease.

Although the OCC issues each listed option contract which

is bought and sold by options participants, it does not act as

a dealer. A listed option is created when a _person makes a

sale of an option contract in an opening transaction. The obligation

of the seller of a call option to deliver stock upon payment of

the exercise price runs to the OCC, and the OCC is obligated to

pay him the exercise price if the option is exercised. The buyer

of a call option is obligated to pay the OCC the exercise price

if he chooses to exercise, and the OCC is then obligated to deliver

the underlying stock.

The seller of any option is commonly referred to as the writer

of the option contract and is said to be "short" the option. The

buyer is the holder of the option and is said to be "long" the

ootion. The original purchase or sale of a contract is an "opening"

transaction, because it opens up a new long or short _~osition.

The subsequent buying back of an identical option, or the sale of

an option being held, is referred to as a "closing" transaction.

For every opening sale transaction in listed options there is a

ourchase transaction. If a writer of an option wishes to close out

his .~osition without awaiting exercise or expiration, he may do so

by buying, in a closing purchase transaction, an option identical

to the one he sold. Similarly, a holder of a listed option may

close out his long .position by entering a closing sale transaction.

Because the OCC stands .between writers and holders of options, there

is no need for an o_Dening writer to sell to an opening buyer. Instead,

an opening writer may sell to a buyer closing out a short position.

At any given time, however, the total obligations of writers of

listed options owed to OCC are equal to the total obligations

of the OCC to holders of the listed options. Data from the CSOE

shows that on a cumulative basis from the inception ok options

trading on that exchange in 1973 through the expiration of CBOE’s

November 1977 series, 68.1 oercent of opening purchase transactions

in calls by holders other than marketmakers were closed in the course of

trading on CBOE, 5.1 percent i__/ were exercised and 27.1 percent were

allowed to expire (see Figure i).

2. The Options Contract

A stock option gives the holder either the right to buy or the

right to sell a smecified number of shares at a specified price

("strike orice") of a designated underlying stock during the life

of the option. An option giving the holder the right to buy the

underlying stock is known as a "call option," because it gives

the holder the right to call upon the person who sold the option

to deliver the designated underlying stock upon payment of the

exercise price. .An ootion giving the holder the right to sell

the ~derlying stock is known as a ’~put option," because it gives

the holder the right to put the underlying stock to the seller

of the option, and the writer is then obligated to _may the stated

exercise price for the stock. The most significant terms of an

option include the number of shares receivable or deliverable

on exercise of the option, which is usually i00 shares, the expiration

date, the underlying security and the exercise price. An option

"premium" is the amount of money that an option buyer pays and

an option seller receives [or an option contract.

Listed option contract prices are quoted based on i) the under-

lying security, 2) the expiration month and 3) exercise price. For

example, an IBM Jan 280 call option refers to an ootion to buy i00

i/ OCC data show that most exercises are for the account of memberfirms.

Closing SalesM~turity Call Put

Grou~p___ Series Series

FIGURE 1

MODE OF LIQUIDATIONS OF LONG POSITIONS*IN CBOE LISTED OPTIONS

1973-1977

Percent of Opening Purchases

ExercisesCall PutSeries Series

ExpirationCall PutSeries Series

1973July 73.3 -- 7.9 -- 16.2Oct. 77.4 -- 6.3 -- 13.7

1974Jan, 58.2 -- 3.9 -- 36,0Apr. 59.6 -- 3.7 -- 33.7July 49.9 -- 0.6 -- 48.2Oct. 52.9 -- 1.0 -- 45.2

1975Jan. 70.0 -- 3.7 -- 25.6Apr. 84.8 -- 7.5 -- 6.7July 71,4 -- 4.2 -- 23.3Aug. 41.8 -- i.i -- 58.5Oct. 73.1 -- 4,8 -- 23.6Nov, 60.4 -- 5.3 -- 34.6

1976Jan. 75.9 -- 8.3 -- 16.9Feb, 80.1 -- 7.2 -- 11.2Apr, 76.4 -- 4,0 -- 17.5May 66.8 -- 4.1 -- 30.4July 79.9 -- 6.5 -- 15.1Aug. 61.1 -- 4.9 -- 35.2Oct, 67.8 -- 5.1 -- 28.4Nov. 55.7 -- 6.4 -- 39.2

1977Jan. 68.8 -- 5.6 -- 26.3 --Feb. 60. I -- 6.1 -- 34.0 --Apr. 55.0 -- 3.8 -- 41.8 --May 61.3 -- 8.1 -- 31.0 --July 66.4 -- 5.8 -- 28.3 --Aug. 60.9 72.3 5.9 5.5 33,1 23.6Oct, 58.5 82.1 3.1 4.4 38.4 10.9Nov, 61.7 75.8 6.3 5,8 32.9 18,3

Expired Series1973-1977 68.1 80.7 5.1 4,7 27.1 12.6

Data are for public customer and firm proprietary accounts. Marketmaker opening and closingtransactions are not distinguished for reporting purposes and are therefore excluded from thetable. Because of occasional coding errors, total liquidations (closing transactions, exercisesand expirations) do not necessarily equal opening purchases.

SOURCE: CBOE Market Statistics, various issues.

shares of IBM common stock at 280 per share (or an aggregate of

$28,000 plus transaction costs) until the following January. An

IBM April 280 call option would refer to the same rights until

the following April.

The rights and obligations under an option contract end on its

expiration date. The expiration time for listed options has been

standardized by the ootions exchanges and is 11:59 o.m. eastern time

on the Saturday following the third Friday in the month in which the

option expires. Options, however, cannot be purchased or sold after

the conclusion of trading rotations, which commence at 3:00 o.~. eastern

time on the business day before expiration in order to ~ermit the OCC

to handle the exercise of expiring options. 2/ All listed options

of the same type -- that is, either puts or calls -- covering the same

underlying security are called a "class of options," and all options

of the same class having the same exercise price and expiration

date are called a "series of options."

Each class of options fits within one of three expiration cycles

which establish the month in which the option contract will expire.

The three expiration cycles are as follow~s:

2~/ For procedures regarding tender of exercise notices, see OCCProspectus (October 16, 1978) at 28-29.

~piration Cycle Exoiration Cycle Exoiration Cycl~

January February Y~rch

April May June

July August September

October November December

New series are generally created with a new expiration month

for a nine-month life when an old series expires. Consequently,

options for only three expiration months are outstanding at any

one time. The exercise price for a new series of options is fixed

in relation to the price of the underlying security at the time the

trading in the new series begins. Exercise orices are generally, but

not always, fixed at five-~oint intervals if the underlying security

is trading below $50 a share, at ten-point intervals if the underlying

stock is trading between $50 and $200 a share, and 20-~oint intervals

if the underlying stock trades above $200 a share. Generally, when

trading is to be introduced in a new expiration month an options

exchange selects two exercise prices surrounding the then current

market price. For examole, if the underlying security trades at

27, new series would be opened at 25 and 30. Additional new

series are also usually introduced whenever the price of the stock

moves up or down to the midooint of the next approoriate 5, i0,

or 20-point interval from the exercise prices of existing contracts.

For example, the price of Ballv Manufacturing Cormoration stock,

which is listed on the ~4YSE, had traded between January and September 20,

1978, at highly fluctuating prices ranging from a low of 15

per share to a high of 71-3/4 per share and closed, on September

20, 1978, at 40-3/8. On September 21, 1978, the Wall Street Journal

reported the following prices of Bally options on the CBOE. Due

to the stock’s great price volatility during the year, new options

series were frequently added. Such fluctuations in the prices of

stocks underlying options, however, are rare occurences.

Ball~_~OPtion Prices on CBOE on September 20, 1978

- Nov. - - Dec. - - May -

Option Price Vol. Cost Vol. Cost Vol. Cost

Bally ...15 1 38-1/4 b b b b

Bally ...20 3 33-1/4 b b bo b

Bally ...25 21 28-3/4 a a b b

Bally ...30 a a 9 19 b b

Bally ...35 116 15 1 14 b b

Bally ...40 193 11-1/8 82 14 52 20-1/4

Bally ...45 283 9-1/4 60 9-1/2 122 13

Bally ...50 1411 6-1/2 131 6-1/2 156 11-1/2

Bally ...60 2113 3-7/8 241 6-1/2 207 8-1/4

Bally ...65 3021 i-5/8 490 4-1/8 225 5-3/4

Price refers to the exercise price of the option.

Volume refers to the number of contracts traded onSeotember 20, 1978 in the particular ootion.

Cost refers to the premium or purchase price at whichan oDtion traded r~ the CBOE on September 20, 1978divided by th� ¯ .~ of shares the option represented.

Close refers to . closing price for Bally Manufacturingstock on the NYSE < September 20, 1978.

a. - indicates the option was not traded on September 20,1978

bo - indicates no option was offered.

Close

47-3/8

47-3/8

47-3/8

47-3/8

47-3/8

47-3/8

47-3/8

47-3/8

47-3/8

47-3/8

3. Stock Price Considerations in Listed ODtions

Opt. ions can be used as a substitute for short-term

stock trading and as a means of transferring certain of the risks and

_Votential rewards of short-term stock price movements from the options

seller to the options buyer. Various strategies can be used to accomplish

this:

An investor who believes a stock will increase in orice can (I) buy

the stock; (2) buv a call; or (3) sell a put. An investor who believes

a stock will decrease in price can (i) sell stock short; (2) sell a

call; or (3) buy a put.

The buyer of stock benefits from any increase in price in excess

of his transactions costs and bears the full risk of loss in the event

of a market decline. Transaction costs include commission charges and

any interest that must be paid if stock is ourchased on margin. While

a call option buyer and a out option seller benefit from a stock price

increase, their risk and reward positions are different.

The call option buyer:

Has the right to buy the underlying stock;

Does not profit until the price of the underlyingstock increases sufficiently to cover the premiumfor the call option plus transaction costs;

Limits his risk of loss to premiums paid plustransaction costs.

The put option seller:

Has the obligation to buy the ~anderlying securityon exercise of the option

Limits his profit to the premium received on thesale of the option, less transactions costs;

Limits his risk of loss only to the extent of themarket price decline of the underlying securityduring the life of the option, a portion of whichwould be offset by the premiums received less trans-action costs ("net premiums").

Similarly, the risk-reward positions of a call option seller and a

put option buyer are different in the event of a stock orice decline.

The call option seller:

Has the obligation to deliver the underlying stockon exercise of the option;

Limits his profit to the oremium received onsale of the options, less transaction costs;

Limits his risk of loss only to the extent thatthe market price increase of the underlyingsecurity during the life of the option is off-set by the net premium received.

The put option buyer :

Has the right to deliver the underlying stock;

Has profits only to the extent the price ofthe underlying stock declines in an amountgreater than the premium for the put optionplus transaction costs;

Limits his risk of loss to the premiumpaid plus transaction costs.

4. Short-Term Character of Omtions Tradinq

Although listed options may have a maximum term of nine months,

most options are written for shorter terms. Indeed, the very short-

term horizon of ootion traders is evident from the distribution of out-

standing ootions -- called open interest -- and contract volume by

expiration month. Statistics for 1977 indicate that 50 to 60 percent

of o~en ~ositions are in ootions with less than 3 months to expiration;

over 70 percent with less than 4 months and 90 percent with less than

6 months (see Figure 2). Similarly, over 60 percent of contract volume

usually appears to be in options with less than 4 months to expiration (see

Figure 3). Even greater concentration of interest and volume exists

for some individual classes of options. For example, data for Eastman

Kodak show that nearly 70 ~ercent of May, 1978 volume in Eastman Kodak

options was in contracts expiring in June, 1978.

FIGURE 2

PERCENTAGE OF OPEN INTEREST IN EXCHANGE TRADED CALL OPTIONSBY MONTHS TO EXPIRATION

Months to Expiration

Less Than1977 3 Months 4 Months 5 Months 6 Months 7 Months 8 Months 9 Months

( Cumulative Percent)

Jan. 60.0 75.3 75.6 92.2 98.2 98.3 I00.0

Feb. 62.0 62.4 83.6 92.6 92.8 99.1 100.0

Mar. 53.7 76.1 86.1 86.3 96.6 99.9 100.0

Apr. 56.7 71.0 71.4 90.0 96.9 97.1 100.0

May 56.9 57.6 80.8 91.1 91.5 99 .I 100.0

Jun. 49.2 73.9 85.3 85.8 96.8 98.9 100.0

Jul. 57.0 72.7 73.5 91.0 97.1 97.5 100.0

Aug. 60.5 61.6 83.1 92.2 92.8 99.0 100.0

Sep. 54.3 77.5 87.6 88.3 97.3 i00.0 I00.0

Oct. 60.0 74.5 75.5 91.9 97.7 98.0 100.0

Nov. 61.7 63.0 84.2 92.8 93.2 99.3 100.0

Dec. 56.5 79.6 88.8 89.5 97.8 99.9 I00.0

SOURCE: Options Clearing Corporation

FIGURE 3

PERCENTAGE OF CONTRACT VOLUME IN EXCHANGE TRADED CALL OPTIONSBY MONTHS TO EXPIRATION

1977

Months to Expiration

Less Than3 Months 4 Months 5 Months 6 Months 7 Months 8 Months 9 Months

(C~nulative Percent)

Jan. 37.0 70.4 80.3 80.6 93.6 98.1 98.3

Feb. 49.2 63.5 64.0 81.8 89.5 89.7 98.8

Mar. 51.0 51.6 73.7 82.2 82.4 94.9 99.9

Apr. 31.1 64.1 73.0 73~3 90.1 96.1 96.3

May 50.6 64.4 64.9 82.6 90.3 90.6 98.9

Jun. 53.4 54.6 76.2 84.5 85.1 95.8 99.7

Jul. 32.5 67.8 77.5 78.2 92.1 96.6 97.1

Aug. 52.3 66.4 " 67.2 83.7 91.0 91.5 98.7

Sep. 53.0 53.9 76.8 84.6 85.2 95.8 99.9

Oct. 33.4 67.8 76.3 77.0 92.1 97.2 97.5

Nov. 55.5 68.4 69.3 86.1 92.3 92.7 99.2

Dec. 57.8 59.7 80.9 87.2 88.1 97.0 99.9

SOURCE: Options Clearing Corporation

5. Transaction Costs o

The short-term nature of most options contracts means that trans-

actions costs can have a significant effect on the profitability of

options transactions. The listed options markets have substantially

reduced the transactions costs of trading options. A study by Black and

Scholes of conventional OI~ options transactions for the period 1966-1969

concluded that transactions costs effectively reduced the rate of return

of call buyers from 33.3 percent to 8.3 percent. In contrast, the rate

of return of call writers was reduced only from 8.6 percent to 6.6 percent.

On the basis of this research they anticipated that if the options markets

could be made more efficient, and less costly for call buyers, the demand

for options would probably increase. 3/

Transaction costs are now substantially less in listed options

than they had been in conventional OTC options. In addition, listed

option transaction costs, if considered without regard to transaction

costs that may be incurred as a result of stock trading that is related

to ootions tradinq, are less than the charges for trading stock in shares

eq.uivalent to that covered by an option contract. Although competitive

commission rates mean that transactions can be entered into at different

charges at different firms, the published commission charges of ten large

retail brokers and one representative discount broker illustrate the current

costs of options trading ms compared with trading directly in the stock

(see Figure

~3/ Black, Fischer, and Scholes, Myron, "The Valuation of OptionsContracts a~d A Test of Market Efficiency," The Journal ofFinance, May, 1972, Pp. 414, 416.

Figure 4

SAMPLE COMMISSION CHARGES FOR TEN LARGEFULL-SERVICE BROKERS AND ONE DISCOUNT BROKER

(amounts in dollars)

PERCENT PERCENT PERCENTi00 SHARES OF 500 SHARES OF 1 CONTRACT* OF

FULL SERVICE BROKERS @$40/SHARE VALUE @$40/SHARE VAUJE @$4/CC~TRACT VALUE(Amount) (Amount) (Amount)

1 75.30 1.88 300.00 1.50 25.00 6.25

2 74.24 1.86 306.56 1.53 27.50 6.88

3 74.90 1.87 307.75 1.54 25.00 6.25

4 74.00 1.85 303.00 1.52 25.00 6.25

5 75.86 1.90 314.73 1.57 26.75 6.69

6 74.90 1.87 265.36 1.33 26.75 6.69

7 68.00 1.70 292.00 1.46 25.00 6.25

8 70.18 1.76 316.95 1.58 15.84 3.96

9 75.03 1.88 306.78 1.54 25.00 6.25

i0 74.00 1.85 310.00 1.55 25.00 6.25

DISCOUNT BROKER

ii 44.79 1.20 189.29 .95 30.00 7.50

* IN M~T CASES, THE CO~MISSION CHARGE FOR ONE CONTRACT IS THEMINIMUM COMMISSION CHARGE FOR A TRANSACTION. BROKER’S FIGURESFOR THE DISCOUNT BROKER ASSUME A LIMIT ORDER RATE.

SOURCE: OPTIONS S~ODY (~OESTIONNAIRE AND BROKER PUBLISHED RATESCHEDULES.

5 CONTRACTS@$4/CONTRACT

(Amount)

74.80

80.78

78.54

74.80

81.11

80.03

77.00

74.80

75.80

87.69

56.55

PERCENTOF

VALUE

3.74

4.04

3.93

3.74

4.06

4.01

3.85

3.74

3.79

4.38

2.83

Although the commissions on options transactions, as a proportion

of the amount of money involved in a transaction, are higher than

for stock, the dollar amount of commissions on an option contract for

1 call to buy I00 shares of stock is about one-third as large as the

commission on a i00 share transaction in the underlying stock. Because

most brokers have a minimum commission charge, however, a better

comparison might be 5 contracts for which the options commission

charges are roughly one-fourth the co~ission on a 500-share stock

transaction. 4__/ Commissions, of course, would be different on options

add stock trades at different prices than those used in Figure 4,

but the dollar amount of commissions on an option will be less than

on a stock trade in an equivalent number of shares underlying the

option. Some discount brokers have advertised rates as low as $12.50

per option contract for fewer than five options, and $2.50 - $8.50

per contract for orders of five options or more; but such rates

may be set purposely low to attract customers with a large volume

of orders.

4/ Moreover, if the options expire worthless, the loss is automaticand there is no sale commission involved, whereas a stockcommission is incurred on the sale of a stock at a loss orprofit.

CorLmissions and cow,mission equivalents (retail mark up) affect

mot~ the prorltaOillty of a transaction and the incentives of broker-

uealers ~%~ tnelr registere~ representatives in reco~ending invest-

~[~nts to t~elr customers, as is descrioe~ in r~re detail below in

chapter V.

b. Options Prlcing Models

~s ~n~cated above, the options contract serves to unbundle the

risks and potential rewards associated with short-term stock price

r, ovements. ’l~e options price is the market valuation of the oundle of

r~gnts t~at are being transferred. C~ief anong these is t]~e right to

~enerlt from or limit losses from short-term stock price fluctuations.

The perceive~ prooability of significant stock price changes will

often re[lect the past snort-term price movements of the stock.

bo~|e stocks trade wlt[lln relatively narrow s~]ort-tem~ price ranges,

whereas ot~er stocks are ~ore volatile. ~br exm-~ple, the Wall Street

Journal reported on December 12, 1978, t]~at for the 52 prior weeks

}m~erxcan Telephone and ’l’elegraph traded between 56-7/8 and 64-5/8 a

snare and closed on bece~Joer II, 1978 at 61 per snare. However,

l’~nesota ~rning and Manu[acturing C~npany ("3M") had traded during

t]~s per~o~ Oetween 43 ar~ ~6 a share and closed on Decemmer Ii, 1978~

at bl, £r all ot]~er _~actors coul~ ~e held constant, the premium for

~n oi~tion usually would be greater ~or a stock which is expected to

~ave volatlle shoru-term prlce movements than the premium for an option

rot- a ~toc~ wn~cn Is expected to trade within a narrow r~ge during the

lzre or ~e optzon. ~ccordingly, ~e volatil~ties of AT&T a~ 3M may

help to explazn wh~ A~I’&T Duly 60 options closed on ~ce~r II, 1978,

at s-3/~ whereas ~e 3~ Juzy 6U options closed at 7-3/8. LiKewise, if all

other factors could ~ held constant, the price of an option would decline

as ~e contract approaches maturity. Thus, on ~ce~r li, 1978, ~e

]~’ Jan b0 optlons closed at 3-3/b ~zle the 3~’~ July 60s closed at 7-3/8.

blmllarlff, I~ all otl~er factors could be held constant, ~e price of an

OptlOll WOUld ~ncrease or decrease as the price of the underlying stock

r~uctuates ~ro~-~d ~e option exercise price. T~e ~unt of ~e increase

or Uecrease, ~[ ~y, would of course de~nd u~n the perceived probability

t~at ~e st~k would trade at an advantageous pE~ce in relation to the

exercise £r~ce at expiration. ~br exm~ple, if a call option had an exercise

price or %bu wltn one week left to expiratzon, a ~vement in ~e price

o[ ~e stock from 4U to ~I woui~ probably have no effect on the price

or course, all ractors cannot ~ held constant, and the prices

or optzo~s ~erlect ~e c~£1ex interrelation of all of ~e a~ve

factors as well as additional [actors tnat apply in a free market

which ~-erlects ~e ]udgmenzs of ~e various participants. Neverthe-

less~ m~y professional traders and arbltra~euEs wlt~ low or no t[ans-

actzons costs nave develo~d optlons priczng ~u~els based u~n these basic

principles and upon other factors which they deemed relevant. This is

done in an attempt to identify options which appear to be under or over-

valued in relation to other options and to the stocks, in anticipation

that they will profit if these pricing discrepancies disappear and to

prevent paying prices that are too high or accepting prices that are too

low. Computers are normally used because of the multiplicity of relevant

factors, many of them generated by constantly changing conditions in the

securities markets.

The most widely known options pricing model is the theoretical valuation

formula developed by Fischer Black and Myron Scholes from which most current

options pricing models have been derived. The Black-Scholes formula was

developed from the principle that options can be used to eliminate market

risk from a stock portfolio. This theory assumes that efficient option

pricing would result in returns on options portfolios equal to the risk-

free interest rate available on investments in U.So government securities.

Their pricing model was developed using European options which are exercisable

only at maturity and has been revised, in part, because it assumed factors

which are not characteristic of listed ootions, including (i) no transactions

costs; (2) no dividends; (3) the option would be exercised on only the

final day before its expiration; (4) there were no restrictions on short

selling; and (5) various assumptions about the characteristics of stock

prlce i~mvements. 5/ Nonetheless the Slack-Scholes options pricing model

serves to illustrate ~]ow options pricing n~dels work.

’llne BlacK-~cnoLes mathematical options pricing model requires five

items of Infor]~tlon to c~;~pute an estilmate of an option’s theoretical

value at any point in time: (i) stock price; (2) time to maturity;

(s) exercise price; (4) ris~ free interest rate; and (5) probable volatility

o£ t~e stocK. 6__/ All these factors, except volatility, are readily

Uetermlnable as of a particular point in time. In ~ost computer pricing

im~e±s t]~e tuture volatility of t]~e stock is estimated based on its past

volatility.

The blacK-ScNoles or similar options pricing models are also used

to estimate the dolLar-for-dollar sensitivity of an option’s price to

~ove~i~nts or the price in the underlying security at any point in time.

Fr~clng ~Jels hold constant the factors ot;]er than stock price that affect

t~e value of an option w[]ile estimating the relationship of changes in

t~e price of h~e option relative to changes in tile price of the stock.

Tn~s estL~mte of the ratio relationship between t~e dollar change in the

Fr~ce ot t~e option and t~e dollar change in the price of the stock is

called the "delta factor." The delta factor of a call option can range

6__/

olaCK, Fischer and Scholes, Myron, "The Pricing of Optionsand Corporate Liabilities" qhe Journal of PoliticalEcon~i~f, ~lay/June 1973, p. 640.

slacm, F~scher, "Fact and Fantasy In the Use of Options,"~nanclal ~al~st Journal, Duly-August, 1975, p. 36.

from 0 to plus 1.00. The delta factor of a put option ranges from 0 to

minus 1.00o If for every one ~oint rise in the price of the equity

security the call option price rises 1/4 point, the call option has a

delta of .25 (and the put option a delta of -.75). If, for every point

rise in the stock the call option price rises 1/2, the call option has

a delta of .50 (and the put option a delta of -.50). 7~/

A long call position and a short put position increase and decrease

in value with the stock. Therefore, these positions have positive delta

factors. The value of a short call position and long out position moves

in the opposite direction of the stock orice. Therefore, these posi-

tions have negative delta factors. A long stock position has a delta value

of 1.00 while a short stock position has a negative delta value of 1.00.

By assigning a delta value to all stock and option positions, a

s~ecialist/marketmaker on the floor of an options exchange can establish

long and short oositions in various series of options of the same class

and in the underlying stock which, if his estimates of the various delta

factors are correct, can result in a position in which any increase or

decrease in value of the stock will be offset by increases or decreases

in his combined options and stock positions. If his calculations are

correct, and his positive deltas are e~ual to his negative deltas, his

overall ~osition wil! be free of risk of stock price movements and his

_7--/ See Black, Fo and M. Scholes, "The Pricing of Options and CorporateLiabilities, Journal of Political Economy (May/June, 1973),642ffo

portfolio is said to be in a "neutral delta position." For example, a

sale of a call option, which has a delta of .5, can be hedged by a purchase

of two call options having a delta of .25. In this case, the value of the

short option’s position will decrease by $.50 for each $i increase in

the price of the underlying stock and the two long options will increase

by $.25 each, or a total of $.50, offsetting the loss on the short option

~osition.

The delta factor changes as the price of the underlying security

and the other factors that determine the price of the option change.

Usually the changes will be small on a day-to-day basis. The exception

occurs during large stock price movements when, apparently, the

statistical reliability of estimates of delta becomes suspect. How-

ever, through the use of options as hedges, portfolio managers have

sought to reduce or eliminate virtually all of the market risk on their

portfolios. However, as the market risk is reduced, the theoretical

rate of return is also reduced until it approaches the risk free interest

rate, a return which can be approximated by investing directly in U.So

government securities.

While the computer option pricing models illuminate certain of the

factors affecting the pricing of options and can aid in omtions trading

decisions, the chapter on Sales Practices shows how computer-generated

data and certain mathematical relationships have formed the background

for unethical sales practices by broker-dealers and investment advisers

and have been used to add mysticism and unnecessary complexity to options

transactions.

7. Examples of the Effect of Options Contracts

Assmiling that there are no pricing biases or market inefficiencies

wnlcn are disaavantageous to eltner options writers or buyers, 8__/ then the

value o~ the b~dle of risks and potential rewards being transferred under

an options contract should De approxJ]nately equal except for commissions

and other transactions costs. An example of how an options buyer and options

seller may rare during the life of a seven-month options contract can help

~e~onstrate t]~e e[rect of the options contract on both buyer and seller

during a ~erlo~ of snort tem~ price ~)vements in a hypothetical situation,

ass~mg that Ootiq ti~e buyer and seller hold the contract until expiration.

As indicated amove, however, nearly all options market participants close

out their options positions in the secondary market prior to expiration.

’±’his assumption is useful for exposition purposes, out studies indi-cate t]~at In the real world, pricing ineificiencies and biases doexist. ~or example, in a study of t~<~ options, Black and Scholesround that t~rougn pricing Diases which favored the seller, buyerse£rectively pald all of the transactions costs necessary for mainten-ance ot the market. See Black and Scholes, note 3, p. 12 above,at pp. 413-417.

~Iso, studies Dy Goul~ and Galai, and Klemkosky and Resnick suggestthat t]~eoretical put and call parity is violated by systematicdiverHence of put and call prices in the real world. Listed optionsnave r~uced these divergences and usually transactions costs in andout preclude profitable arbitrage by most public investors. Whileliste~ options nave r~uced transactions costs, there is no reasonto asst~e t~at bias no longer exists, especially with restrictionson Iiste~ puts and t]~e nigher costs that are thereby imposed onarbitrage activities. See Goul~, J. P. and Galai, D., "TransactionsCosts and Put and Call Prices," Journal of Financial Economics, (July1974), Galas, Dan, "’Tests or ~arKet Efficiency of the Chicago BoardOptions Sxcnange," Journal of Business, (April 1977) and Klemkosky,~,ooert C. and ~{esnick, Bruce G., "Put-Call Parity and Market Efficiency"[~resented to Sout~ern Finance Association Annual Conference, November1978, Washington~ D.C.

a. Call Option

Assume, for examole, that XYZ stock is selling at $50 a share on

October 20, and that a call option on XYZ expiring in May and exercisable

at 50 trades at 6o The writer of this option will receive $600 per contract

paid by the buyer before any allowance for transaction costs. Of course,

both sides in this transaction would have to pay commissions. If the writer

owns the i00 shares of XYZ (a covered option), he will be in a better

~osition than he would have been without the combined stock/option position

anytime the stock trades at less than 56 but above 44 per share, after

allowance for transaction costs (see Figure 5). The writer of the call

option, however, may be called upon to deliver the shares anytime, although

exercise is likely only when the stock price is above $50. If the writer

of the option does not own the underlying stock (an uncovered option)

or an offsetting option, the writer assumes the risks of rises in the

market price of the underlying stock and will be required to acquire and

deliver the underlying stock, much like a short-seller, if the option

is exercised against him. In exchange for the options premium, however,

the writer of the option gives up to the ootion buyer the right to gains

through exercise or resale of the contract. This would normally only occur

if XYZ sells above $50 a share. The covered writer retains the risks of

ownership if XYZ declines in orice. The uncovered writer is exposed to

unlimited risks on the upside, but none on the downside.